As Large Language Models (LLMs) gain great success in real-world applications, an increasing number of users are seeking to develop and deploy their customized LLMs through cloud services. Nonetheless, in some specific domains, there are still concerns regarding cost and trade-offs between privacy issues and accuracy. In this study, we introduce a cost-effective and self-adaptive LLM shaking tuning and recovery mechanism, named CypherTalk. With carefully designed horizontal and vertical shaking operators, we can achieve comparable accuracy results with SOTA privacy-preserving LLM schemes using Cryptography-based or Differential Privacy-based methods. Experiments also show that with the CypherTalk framework, users can achieve reliable accuracy when using optimized shaking operator settings. To our best knowledge, this is the first work that considers cost, and trade-off between model utility and privacy in LLM scenarios.